Mean curvature properties for p-Laplace phase transitions | Zendy

Berardino Sciunzi | Zendy; Enrico Valdinoci | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Mean curvature properties for p-Laplace phase transitions

Author(s) -

Berardino Sciunzi,

Enrico Valdinoci

Publication year - 2005

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/31

Subject(s) - mathematics , hypersurface , mean curvature , laplace operator , curvature , mathematical analysis , phase transition , zero (linguistics) , viscosity solution , kinetic energy , laplace transform , type (biology) , pure mathematics , mathematical physics , geometry , classical mechanics , thermodynamics , physics , ecology , linguistics , philosophy , biology

This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of $p$-Laplacian type and a double well potential $h_0$ with suitable growth conditions. We prove that level sets of solutions of $\Delta_p u=h_0'(u)$ possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research